We present a new trilevel optimization algorithm to solve the robust two-stage unit commitment problem. In a robust unit commitment problem, first stage commitment decisions are made to anticipate the worst case realization of demand uncertainty and minimize operation cost under such scenarios. In our algorithm, we decomposed the trilevel problem into a master problem and a sub-problem. The master problem can be solved as a mixed-integer program and the sub-problem is solved as a linear program with complementary constraints with the big-M method. We then designed numerical experiments to test the performance of our algorithm against that of the Benders decomposition algorithm. The experiments shows that our algorithm performs consistently better than the Benders approach.
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